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Meixner-Pollaczek polynomials and the Heisenberg algebra
Tom H. Koornwinder
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TLDR
In this paper, an alternative proof is given for the connection between a system of continuous Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56, 2445 (1986); J. Math. 28, 509 (1987)].Abstract:
An alternative proof is given for the connection between a system of continuous Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56, 2445 (1986); J. Math. Phys. 28, 509 (1987)]. The continuous Hahn polynomials turn out to be Meixner–Pollaczek polynomials. Use is made of the connection between Laguerre polynomials and Meixner–Pollaczek polynomials, the Rodrigues formula for Laguerre polynomials, an operational formula involving Meixner–Pollaczek polynomials, and the Schrodinger model for the irreducible unitary representations of the three‐dimensional Heisenberg group.read more
Citations
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Generalized Zernike or disc polynomials: An application in quantum optics
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The Meixner-Pollaczek polynomials and a system of orthogonal polynomials in a strip
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Roderick Wong,Zhao Yuqiu +1 more
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Weyl-ordered polynomials in fractional-dimensional quantum mechanics
M. A. Lohe,A. Thilagam +1 more
TL;DR: Weyl-ordered polynomials in the momentum and position operators P, Q which satisfy the R-deformed Heisenberg algebra, representations of which describe quantum mechanics in fractional dimensions are studied in this article.
References
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Book
Groups and geometric analysis
TL;DR: Geometric Fourier analysis on spaces of constant curvature Integral geometry and Radon transforms Invariant differential operators Invariants and harmonic polynomials Spherical functions and spherical transforms Analysis on compact symmetric spaces Appendix Some details Bibliography Symbols frequently used Index Errata.
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Convolutions for orthogonal polynomials from Lie and quantum algebra representations.
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The Hahn and Meixner polynomials of an imaginary argument and some of their applications
TL;DR: In this article, the Hahn and Meixner polynomials of a discrete variable are analytically continued in the complex plane both in variable and parameter, leading to the origination of two systems of real polynomial systems orthogonal with respect to a continuous measure.